The University of Punjab was established at Lahore in 1882 to reduce the burden of the university of:

The correct option is Calcutta.

To understand why this is correct, we can look at the historical development of higher education in British India during the 19th century:
1. Establishment of the Presidency Universities (1857): Following Wood's Despatch of 1854, three major universities were established in 1857 in the presidency towns of Calcutta, Bombay, and Madras. Among these, the University of Calcutta had an exceptionally large geographical jurisdiction, covering almost the entirety of Northern and Eastern India, including the Punjab region.
2. The Growing Academic Burden: As the number of schools and colleges in Northern India grew, the administrative and examination burden on the University of Calcutta became overwhelming. Managing affiliations, curricula, and examinations for institutions thousands of miles away was no longer sustainable.
3. Establishment of the University of the Punjab (1882): To decentralize the educational administration and address the local demands of the Punjab province, the University of the Punjab was established at Lahore in 1882. It became the fourth university established in British India, directly taking over the academic jurisdiction of the Punjab region and thereby significantly reducing the administrative load of the University of Calcutta.